Consensus with Preserved Privacy against Neighbor Collusion

Abstract

This paper proposes a privacy-preserving algorithm to solve the average consensus problem based on Shamir's secret sharing scheme, in which a network of agents reach an agreement on their states without exposing their individual state until an agreement is reached. Unlike other methods, the proposed algorithm renders the network resistant to the collusion of any given number of neighbors (even with all neighbors' colluding). Another virtue of this work is that such a method can protect the network consensus procedure from eavesdropping.

Network Consensus with Privacy: A Secret Sharing Method

“…Moreover, we say that an algorithm reaches average consensus with an exact privacy degree p, if in Problem 1 the function x ∞ = 1 N N i=1 x i (0). In our previous work [49], we address average consensus problem with a privacy degree instead of an exact privacy degree, i.e., there is no guarantee that the privacy x i (t) can be reconstructed from many enough messages {R i t (x i (t))} ∈I . 1 Here we insist that x∞ can be expressed as a non-trivial function of the initial states, i.e., x∞ = G(x 1 (0), .…”

“…Several methods have been developed to achieve, at least to some extent, privacy-preserving consensus algorithms. Methods include masking the true state by adding deterministic offsets to the messages [44], [45], [46], [47], [48], [49], adding random noise to the messages transmitted amongst nodes [50], [51], [52], [53], [46], and using various encryption schemes [54], [10], [55]. Another interesting method for computing separable functions without disclosing nodes' privacy appeared in [56], where agents exchange a set of samples drawn from a distribution depending on their true state, and the number of these samples can be tuned by a trade-off between the accuracy and privacy level of the algorithm.…”